In various control engineering applications, it is desired to regulate some physical variable throughout the length, area, or volume of a medium. Examples can include elimination of vibration in flexible, solid material structures, disturbance elimination in fluid flow, uniform temperature regulation throughout a fluid pool, etc. Until recently, the typical interface between the medium and the controller consisted of a relatively small number of sensors and actuators at fixed locations. The sensors continuously monitor the actual state of the relevant physical variables at their respective locations while the actuators continuously act in real time on the medium in response to controller logic. The controller, which typically comprises a microprocessor, determines the appropriate action on the basis of the sensor readings, predetermined control objectives, and the control algorithm logic.
Recent advancements in micro-electro-mechanical systems (MEMS) have produced microscopic devices with actuating, sensing, computing, and/or telecommunication capabilities. It is preferred to distribute a large array of MEMS in a spatial configuration in order to enhance capabilities for control. Examples can include distributed flow control for drag reduction, xe2x80x9csmartxe2x80x9d mechanical structures such as a building able to automatically respond to earthquakes, and cross-directional control of large scale paper machines.
However, the increased distribution of MEMS throughout a medium to be controlled has created certain control problems. For example, the current speed and memory capabilities of microprocessors are insufficient to process the multiplicity of sensor readings and control the actuators in a meaningful fashion.
Prior model-based controller algorithms having employed the following forms:             ⅆ              ⅆ        t              ⁢                  ψ        K            ⁢              (        t        )              =                    A        K            ⁢              ψ        k                  (          t          )                      +                  B        K            ⁢              y        ⁢                  (          t          )                    xe2x80x83u(t)=Ck"psgr"k(t)+Dkyk(t)
where "psgr"K represents an estimate of the present state of a system at time t, A, B, C, and D represents linear operators acting on the system, u represents a control operator be applied to the estimate "psgr"K, and y represents the output of the system sensed by sensors. The problem with these forms as applied to systems with distributed sensor and actuators is that they do not exploit the spatial dynamics of the system and their structure. Accordingly, a need exists to accurately design controller logic that minimizes quadratic performance criterion in such contexts.
A control system is provided which includes a state estimator including an operator which acts on estimation error through convolution with respect to a spatial variable to generate a state estimate. The control system further includes a control output generator which applies a control operator to the state estimate through convolution with respect to the spatial variable. According to further aspects of the present invention, the operator of the state estimator and the control operator are localized in space, are independent of time, and minimize quadratic objective functions.
Preferably, the control system is controlling a linear shift invariant system, which may be referred to as a spatially invariant system, and is a model-based estimator control system.
A method is also provided for designing a control system which includes the steps of obtaining a system model, computing a transform of the model with respect to the spatial domain, solving linear matrix inequalities to generate auxiliary variables, performing an inverse transform on the auxiliary variables, and computing an estimator operator and a control operator for a model-based estimator control system.
Preferably, the step of computing a transform of the model with respect to the spatial domain is accomplished using a Fourier transform, and the step of solving linear matrix inequalities to generate auxiliary variables is accomplished using algebraic Ricatti equations.
According to yet further aspects of the present invention, the estimator operator acts on estimation error through convolution with respect to a spatial variable to generate a state estimate. A control output generator applies the control operator to the state estimate through convolution with respect to the spatial variable.
According to yet another aspect of the present invention, a control system is provided which includes means for estimating a state including an operator which acts on estimation error through convolution with respect to a spatial variable to generate a state estimate, and means for generating a control output including applying a control operator to the state estimate through convolution with respect to the spatial variable.